4.3.2 problem 2

Internal problem ID [1167]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.4. Page 76
Problem number : 2
Date solved : Tuesday, September 30, 2025 at 04:27:07 AM
CAS classification : [_separable]

\begin{align*} y+\left (-4+t \right ) t y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.064 (sec). Leaf size: 17

ode:=y(t)+(-4+t)*t*diff(y(t),t) = 0; 
ic:=[y(2) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\left (\frac {1}{2}+\frac {i}{2}\right ) \sqrt {2}\, t^{{1}/{4}}}{\left (-4+t \right )^{{1}/{4}}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 20

ode=y[t]+(-4+t)*t*D[y[t],t] == 0; 
ic=y[2]==1; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\sqrt [4]{t}}{\sqrt [4]{4-t}} \end{align*}

✓ Sympy. Time used: 0.180 (sec). Leaf size: 20

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*(t - 4)*Derivative(y(t), t) + y(t),0) 
ics = {y(2): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {\sqrt [4]{-1} \sqrt [4]{t}}{\sqrt [4]{t - 4}} \]